Middle School Math

Topic

First Poster

Last Poster

k a May Highlights and 2025 AoPS Online Class Information

jlacosta 0

May 1, 2025

May is an exciting month! National MATHCOUNTS is the second week of May in Washington D.C. and our Founder, Richard Rusczyk will be presenting a seminar, Preparing Strong Math Students for College and Careers, on May 11th.

Are you interested in working towards MATHCOUNTS and don’t know where to start? We have you covered! If you have taken Prealgebra, then you are ready for MATHCOUNTS/AMC 8 Basics. Already aiming for State or National MATHCOUNTS and harder AMC 8 problems? Then our MATHCOUNTS/AMC 8 Advanced course is for you.

Summer camps are starting next month at the Virtual Campus in math and language arts that are 2 - to 4 - weeks in duration. Spaces are still available - don’t miss your chance to have an enriching summer experience. There are middle and high school competition math camps as well as Math Beasts camps that review key topics coupled with fun explorations covering areas such as graph theory (Math Beasts Camp 6), cryptography (Math Beasts Camp 7-8), and topology (Math Beasts Camp 8-9)!

Be sure to mark your calendars for the following upcoming events:
[list][*]May 9th, 4:30pm PT/7:30pm ET, Casework 2: Overwhelming Evidence — A Text Adventure, a game where participants will work together to navigate the map, solve puzzles, and win! All are welcome.
[*]May 19th, 4:30pm PT/7:30pm ET, What's Next After Beast Academy?, designed for students finishing Beast Academy and ready for Prealgebra 1.
[*]May 20th, 4:00pm PT/7:00pm ET, Mathcamp 2025 Qualifying Quiz Part 1 Math Jam, Problems 1 to 4, join the Canada/USA Mathcamp staff for this exciting Math Jam, where they discuss solutions to Problems 1 to 4 of the 2025 Mathcamp Qualifying Quiz!
[*]May 21st, 4:00pm PT/7:00pm ET, Mathcamp 2025 Qualifying Quiz Part 2 Math Jam, Problems 5 and 6, Canada/USA Mathcamp staff will discuss solutions to Problems 5 and 6 of the 2025 Mathcamp Qualifying Quiz![/list]
Our full course list for upcoming classes is below:
All classes run 7:30pm-8:45pm ET/4:30pm - 5:45pm PT unless otherwise noted.

Introductory: Grades 5-10

Prealgebra 1 Self-Paced

Prealgebra 1
Tuesday, May 13 - Aug 26
Thursday, May 29 - Sep 11
Sunday, Jun 15 - Oct 12
Monday, Jun 30 - Oct 20
Wednesday, Jul 16 - Oct 29

Prealgebra 2 Self-Paced

Prealgebra 2
Wednesday, May 7 - Aug 20
Monday, Jun 2 - Sep 22
Sunday, Jun 29 - Oct 26
Friday, Jul 25 - Nov 21

Introduction to Algebra A Self-Paced

Introduction to Algebra A
Sunday, May 11 - Sep 14 (1:00 - 2:30 pm ET/10:00 - 11:30 am PT)
Wednesday, May 14 - Aug 27
Friday, May 30 - Sep 26
Monday, Jun 2 - Sep 22
Sunday, Jun 15 - Oct 12
Thursday, Jun 26 - Oct 9
Tuesday, Jul 15 - Oct 28

Introduction to Counting & Probability Self-Paced

Introduction to Counting & Probability
Thursday, May 15 - Jul 31
Sunday, Jun 1 - Aug 24
Thursday, Jun 12 - Aug 28
Wednesday, Jul 9 - Sep 24
Sunday, Jul 27 - Oct 19

Introduction to Number Theory
Friday, May 9 - Aug 1
Wednesday, May 21 - Aug 6
Monday, Jun 9 - Aug 25
Sunday, Jun 15 - Sep 14
Tuesday, Jul 15 - Sep 30

Introduction to Algebra B Self-Paced

Introduction to Algebra B
Tuesday, May 6 - Aug 19
Wednesday, Jun 4 - Sep 17
Sunday, Jun 22 - Oct 19
Friday, Jul 18 - Nov 14

Introduction to Geometry
Sunday, May 11 - Nov 9
Tuesday, May 20 - Oct 28
Monday, Jun 16 - Dec 8
Friday, Jun 20 - Jan 9
Sunday, Jun 29 - Jan 11
Monday, Jul 14 - Jan 19

Paradoxes and Infinity
Mon, Tue, Wed, & Thurs, Jul 14 - Jul 16 (meets every day of the week!)

Intermediate: Grades 8-12

Intermediate Algebra
Sunday, Jun 1 - Nov 23
Tuesday, Jun 10 - Nov 18
Wednesday, Jun 25 - Dec 10
Sunday, Jul 13 - Jan 18
Thursday, Jul 24 - Jan 22

Intermediate Counting & Probability
Wednesday, May 21 - Sep 17
Sunday, Jun 22 - Nov 2

Intermediate Number Theory
Sunday, Jun 1 - Aug 24
Wednesday, Jun 18 - Sep 3

Precalculus
Friday, May 16 - Oct 24
Sunday, Jun 1 - Nov 9
Monday, Jun 30 - Dec 8

Advanced: Grades 9-12

Olympiad Geometry
Tuesday, Jun 10 - Aug 26

Calculus
Tuesday, May 27 - Nov 11
Wednesday, Jun 25 - Dec 17

Group Theory
Thursday, Jun 12 - Sep 11

Contest Preparation: Grades 6-12

MATHCOUNTS/AMC 8 Basics
Friday, May 23 - Aug 15
Monday, Jun 2 - Aug 18
Thursday, Jun 12 - Aug 28
Sunday, Jun 22 - Sep 21
Tues & Thurs, Jul 8 - Aug 14 (meets twice a week!)

MATHCOUNTS/AMC 8 Advanced
Sunday, May 11 - Aug 10
Tuesday, May 27 - Aug 12
Wednesday, Jun 11 - Aug 27
Sunday, Jun 22 - Sep 21
Tues & Thurs, Jul 8 - Aug 14 (meets twice a week!)

AMC 10 Problem Series
Friday, May 9 - Aug 1
Sunday, Jun 1 - Aug 24
Thursday, Jun 12 - Aug 28
Tuesday, Jun 17 - Sep 2
Sunday, Jun 22 - Sep 21 (1:00 - 2:30 pm ET/10:00 - 11:30 am PT)
Monday, Jun 23 - Sep 15
Tues & Thurs, Jul 8 - Aug 14 (meets twice a week!)

AMC 10 Final Fives
Sunday, May 11 - Jun 8
Tuesday, May 27 - Jun 17
Monday, Jun 30 - Jul 21

AMC 12 Problem Series
Tuesday, May 27 - Aug 12
Thursday, Jun 12 - Aug 28
Sunday, Jun 22 - Sep 21
Wednesday, Aug 6 - Oct 22

AMC 12 Final Fives
Sunday, May 18 - Jun 15

AIME Problem Series A
Thursday, May 22 - Jul 31

AIME Problem Series B
Sunday, Jun 22 - Sep 21

F=ma Problem Series
Wednesday, Jun 11 - Aug 27

WOOT Programs
Visit the pages linked for full schedule details for each of these programs!

MathWOOT Level 1
MathWOOT Level 2
ChemWOOT
CodeWOOT
PhysicsWOOT

Programming

Introduction to Programming with Python
Thursday, May 22 - Aug 7
Sunday, Jun 15 - Sep 14 (1:00 - 2:30 pm ET/10:00 - 11:30 am PT)
Tuesday, Jun 17 - Sep 2
Monday, Jun 30 - Sep 22

Intermediate Programming with Python
Sunday, Jun 1 - Aug 24
Monday, Jun 30 - Sep 22

USACO Bronze Problem Series
Tuesday, May 13 - Jul 29
Sunday, Jun 22 - Sep 1

Physics

Introduction to Physics
Wednesday, May 21 - Aug 6
Sunday, Jun 15 - Sep 14
Monday, Jun 23 - Sep 15

Physics 1: Mechanics
Thursday, May 22 - Oct 30
Monday, Jun 23 - Dec 15

Relativity
Mon, Tue, Wed & Thurs, Jun 23 - Jun 26 (meets every day of the week!)

0 replies

jlacosta

May 1, 2025

0 replies

J

H

Overly wordy problems

ZMB038 4

N 40 minutes ago by CJB19

Hey everyone, here we can post questions with way to many extraneous words, that are actually easy.
Try to solve the one above yours.
I'll start:
Click to reveal hidden text

4 replies

ZMB038

5 hours ago

CJB19

40 minutes ago

J

H

Math with Connect4 Boards

Math-lover1 7

N 2 hours ago by CJB19

Hi! So I was playing Connect4 with my friends the other day and I wondered: how many "legal" arrangements of Connect4 can be reached at the ending position?

We assume that we do not stop the game when there is a four in a row, and we have 21 red pieces and 21 yellow pieces. We also drop the pieces one by one into a standard 7 by 6 board. We can start the game with any color piece.

https://en.wikipedia.org/wiki/Connect_Four

Initial Thoughts
Attempt to use one-to-one correspondences

7 replies

Math-lover1

May 1, 2025

CJB19

2 hours ago

J

H

9 AMC 10 Prep

bluedino24 44

N 2 hours ago by A7456321

I'm in 7th grade and thought it would be good to start preparing for the AMC 10. I'm not extremely good at math though.

What are some important topics I should study? Please comment below. Thanks! :D

44 replies

bluedino24

May 2, 2025

A7456321

2 hours ago

J

H

Area of Polygon

AIME15 49

N 2 hours ago by Wolfpierce

The area of polygon $ABCDEF$ , in square units, is

IMAGE

$\textbf{(A)}\ 24 \qquad \textbf{(B)}\ 30 \qquad \textbf{(C)}\ 46 \qquad \textbf{(D)}\ 66 \qquad \textbf{(E)}\ 74$

49 replies

AIME15

Jan 12, 2009

Wolfpierce

2 hours ago

J

H

Problem 2, Grade 12th RMO Shortlist - Year 2002

sticknycu 5

N Yesterday at 4:07 PM by P_Fazioli

Let $A \in M_2(C), A \neq O_2, A \neq I_2, n \in \mathbb{N}^*$ and $S_n = \{ X \in M_2(C) | X^n = A \}$ .
Show:
a) $S_n$ with multiplication of matrixes operation is making an isomorphic-group structure with $U_n$ .
b) $A^2 = A$ .

Marian Andronache

5 replies

sticknycu

Jan 3, 2020

P_Fazioli

Yesterday at 4:07 PM

J

H

3rd AKhIMO for University Students, P1

UzbekMathematician 1

N Yesterday at 3:42 PM by KAME06

Source: AKhIMO 2025, P1

There are two circles in the $xy-$ plane centered on the $y-$ axis which are tangent to both the parabola $y=x^2$ and the line $y=2025$ . Determine the lengths of the circles' diameters.

1 reply

UzbekMathematician

Yesterday at 1:44 PM

KAME06

Yesterday at 3:42 PM

J

H

3rd AKhIMO for university students, p4

UzbekMathematician 1

N Yesterday at 2:29 PM by grupyorum

Source: AKhIMO 2025, P4

Define a sequence $a_1, a_2, a_3, ...$ by $a_1=2, a_2=5$ and $a_{n+2}=f(a_n, a_{n+1})$ for all $n \ge 1$ , where $f(x,y)=5(x+y)+2\sqrt{6x^2+15xy+6y^2}.$ Show that $a_n$ is an integer for all $n\ge 1$ .

1 reply

UzbekMathematician

Yesterday at 2:03 PM

grupyorum

Yesterday at 2:29 PM

J

H

Double Integral

namesis 3

N Yesterday at 2:27 PM by Mathzeus1024

The area of integration, $D$ , is defined in plane polar coordinates $(r, \phi)$ by the inequality
$r-2 \leq r \leq r_1$ , where $r_1 = 1 + \cos(\phi)$ and $r_2 = 3/2$ .

Evaluate:

$\iint_D \frac{x+y+xy}{x^2 + y^2} dx dy$

I tried evaluating the integral in polar, with $r$ from $\frac{3}{2}$ to $1+ \cos \phi$ and $\phi$ from $- \frac{\pi}{3}$ to $\frac{\pi}{3}$ but in vain.

3 replies

namesis

Dec 16, 2015

Mathzeus1024

Yesterday at 2:27 PM

J

H

Japanese Olympiad

parkjungmin 8

N Yesterday at 2:22 PM by parkjungmin

It's about the Japanese Olympiad

I can't solve it no matter how much I think about it.

If there are people who are good at math

Please help me.

8 replies

parkjungmin

May 10, 2025

parkjungmin

Yesterday at 2:22 PM

J

H

3rd AKhIMO for university students, P5

UzbekMathematician 0

Yesterday at 2:10 PM

Source: AKhIMO 2025, P5

Show that for every positive integer $n$ there exist nonnegative integers $p, q$ and integers $a_1, a_2, ... , a_p, b_1, b_2, ... , b_q \ge 2$ such that $n=\frac{(a_1^3-1)(a_2^3-1)...(a_p^3-1)}{(b_1^3-1)(b_2^3-1)...(b_q^3-1)}$

0 replies

UzbekMathematician

Yesterday at 2:10 PM

0 replies

J

H

Double integral on polar coordinates

Kurchi 1

N Yesterday at 1:54 PM by Mathzeus1024

How to find the volume inside z=r above r=3+cosθ, with the help of double integral?

1 reply

Kurchi

Jul 2, 2020

Mathzeus1024

Yesterday at 1:54 PM

J

H

Recurrence trouble

SomeonecoolLovesMaths 0

Yesterday at 11:27 AM

Let $0 < x_0 < y_0$ be real numbers. Define $x_{n+1} = \frac{x_n + y_n}{2}$ and $y_{n+1} = \sqrt{x_{n+1}y_n}$ .
Prove that $\lim_{n \to \infty} x_n = \lim_{n \to \infty} y_n$ and hence find the limit.

0 replies

SomeonecoolLovesMaths

Yesterday at 11:27 AM

0 replies

J

H

nice integral

Martin.s 1

N Yesterday at 10:10 AM by Svyatoslav

$\int_0^\infty \left(\frac{1}{\log t}+\frac{1}{1-t}\right)^3 \frac{dt}{1+t^2}$

1 reply

Martin.s

Tuesday at 11:24 AM

Svyatoslav

Yesterday at 10:10 AM

J

H

Sequence and Series

P162008 1

N Yesterday at 9:24 AM by alexheinis

Source: Coaching Test

Let $a_n = 3n + \sqrt{n^2 - 1}$ and $b_n = 2\left(\sqrt{n^2 - n} + \sqrt{n^2 + n}\right)$
If $\sum_{i=1}^{49} \sqrt{a_i - b_i} = A + B\sqrt{2}$ for some integers $A$ and $B.$ Find the value of $A^2 + B^2.$

1 reply

P162008

Tuesday at 6:22 AM

alexheinis

Yesterday at 9:24 AM

J